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I generally try to avoid flamebait, but I saw this article linked off of Twitter. I should have stopped reading after the first section where it's clear that the author is a troll. Evolution and science denialism aside, the misrepresentation of mathematics in the article is inexcusable.

After attacking Darwin and scientific thought in general, an appeal to emotion, he proceeds into a second hand quote from a philosopher on the subject of "fallacies". It's kind of ironic that the inclusion of this quote would serve as an appeal to authority.

Next, he goes into intelligent design saying:

we could find incontrovertible evidence that reality, matter, life, has been designed, but that interpretation of the evidence would be discarded because naturalism dictates the exclusion of anything which might lead outside of a naturalistic explanation.

This is absolutely false. Scientific theories are necessarily falsifiable. If the evidence implied a "design", that's what the scientific theory would be. The fact is that the evidence points to the contrary. Biology shows a picture of "unintelligent design", consistent with a process of genetic mutations occurring over time. The naturalistic explanation is the one that the evidence supports.

Then he claims that Gödel's Incompleteness Thereom proves this.

He managed to get Gödel's basic background information right, but incorrectly describes the Incompleteness Theorem.

From the article:

Any system that is consistent is incomplete.

The consistency of axioms (axioms=assumptions that cannot be proven) cannot be proved from within the system.

Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true,[1] but not provable in the theory (Kleene 1967, p. 250).

For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent.

Notice how the part about "basic arithmetic" is conveniently left out of the definition? That's because the author doesn't want you to know that there can exist axiomatic systems which are both complete and consistent. First-order predicate logic was proven to be both complete and consistent by none other than Gödel himself. Furthermore, saying that the Incompleteness Theorem "utterly [destroyed] atheist Bertrand Russell’s logical system for arithmetic" doesn't give Russell the credit he deserves. Gödel's technique was based on the same idea as Russell's Paradox to begin with. Despite its incompleteness, the development of Russell's work into Zermelo-Fraenkel set theory was an important building block in the foundation of later mathematics. By referring to him as "atheist Bertrand Russell", it's clear that the author is more concerned about religion than the actual mathematics.

Next we have a very weak analogy. He describes three items on a table and says:

Now draw a circle around those items. We will call everything in that circle a system. Gödel’s first theorem tells us that nothing in the circle can explain itself without referring to something outside the circle.

It's true that Gödel's theorem succeeded in "stepping out of basic arithmetic", but here's where that omitted condition of a "formal system capable of basic arithmetic" comes into play. Are a half-full cup of coffee, a fishing pole and a jacket capable of arithmetic? If the answer is no, then Gödel's theorem doesn't apply. Capable of self reference? Maybe if the coffee mug says "I'm a half full cup of coffee" on it.

The analogy of a computer is a much better example. Computer programs are capable of basic arithmetic. What Gödel's theorem implies for computers is that there exist certain programs which are computationally irreducible. The only way to determine the output of such a program is to run it. If we think of Nature like a computer program, the only way to be certain of the future "output" is to let Nature run its course. This result does not prevent science from making conjectures about the structure of Nature, but requires that science adopt a Black-box testing procedure which entails experimentation and observation. There are certainly unanswerable questions in science, such as the precise position and momentum of elementary particles, but evolution isn't one of them. The evidence for evolution is incontrovertible.

The final second shift the analogy to the universe and the claim is that what's outside the universe is unknowable. Just because we can't see what's outside the universe, which would be white-box testing, doesn't mean we can make and test hypotheses about it as a "black-box". The Many-worlds interpretation of quantum theory is one such example which predicts that our universe is but one of many possible universes. Similarly, M-theory predicts the existence of hidden dimensions beyond space and time. Just because some questions are unanswerable, doesn't mean all questions are.

The article ends by claiming that evolution and naturalism are "fallaciously circular", but here's the real circular fallacy:

Author misinterprets Gödel's theorem to imply that all axiomatic systems are incomplete or inconsistent.

Author mistakenly assumes that science is an axiomatic system.

Based on this misinterpretation, author concludes that science must be incomplete or inconsistent.

Since author concludes that complete scientific knowledge is incomplete or inconsistent, author ceases to look for empirical evidence of scientific claims.

Since author ceases to look for evidence, author does not find any evidence.

Since author does not find any evidence, author concludes that scientific knowledge is incomplete.

As a consequence, the author's incomplete knowledge becomes a self-fulfilling prophesy.

This whole article is a Proof by Intimidation. The "average Joe" doesn't know enough about contemporary math and science to go through and verify each detail. The use of mathematics vocabulary in the article is deliberately being used to distract the reader from the real issue -- the overwhelming evidence for evolution. The references to Gödel's Incompleteness Theorem are nothing more than a red herring, and the author even misstates the theorem to boot.

So I noticed a new comment on my old Guild Wars Me/D video, and it enticed me to play again. Unfortunately, the build in the video had been completely changed in a recent patch. Sand Shards no longer deals damage on misses, but instead causes a AoE DoT effect when it ends. Whereas the old version pumped out a lot of damage if there were multiple foes to miss, the new version has lower damage output and causes the AI to scatter even easier. Thus, I set out to see if I could make a new solo build with the same profession combination.

The survivability of the old build was still pretty much intact, but I no longer needed the self-blind of Signet of Midnight due to the change in Sand Shards functionality. I went over to the Zaishen arena and started to play around. What I found was that I could keep myself alive without blind by using a combination of Mystic Regeneration, Mirage Cloak and Armor of Sanctity. I changed the elite skill to Signet of Illusions and reallocated my stat points. This opened up a variety of other options for damage. After some experimentation, I was able to down IWAY with the following combination:

Signet of Illusions - makes all skills use Illusion attribute (16)

Mystic Regeneration, Mirage Cloak. Armor of Sanctity - keep me alive

Channeling - energy management

Mystic Twister, Dust Cloak - additional damage

Faithful Intervention - just another enchantment

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With the proof of concept working, I decided to give it a whirl in PvE. I went to my old Sunspear rep farming spot, East out of Camp Hojanu in Barbarous Shore. Right outside the town are several packs of Heket which are mostly physical damage. Since the packs were only 4 instead of 8 like IWAY, Channeling wasn't return quite enough energy to cover the enchantment maintenance. I switched out Faithful Intervention for Auspicious Incantation for more energy. With the energy problem solved, I didn't really need the blind effect on Dust Cloak anymore and switched it our Heart of Holy Flame to add burning instead. The only problem with this farming spot are the Blue Tongue Heket monks that spawn randomly in the melee packs. I had some success using Backfire on them, but they still could take a while to kill. I decided it would be better to just avoid them altogether.

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Having Signet of Illusions leaves plenty of room for variation in the build, as it can use any skills with an effective attribute of 16. I found that having Armor of Sanctity up was more important than Mirage Cloak in most cases. The damage from letting Mirage Cloak drop and the synergy with Auspicious Incantation made it worth keeping, but it might be possible to do without it in some locations. A Dervish primary could probably use a similar setup and might be able to get away without the energy management skills needed on my Mesmer. Although Fast Casting is kind of nice against the Heket because they like to interrupt. Not bad for a proof of concept, but more damage and a speed boost would be nice.

This article is just for fun and is not targeted toward an audience unfamiliar with the Bleach series. However, if you're a fan of Tite Kubo's Bleach and have never heard Julian Jaynes and the Bicameral Mind I'm hoping that this will provide an entertaining introduction to this daring psychological hypothesis.

[spoiler alert!]

I originally saw the first episode of Bleach on Cartoon Network and have been delightfully following the series ever since. It's about a orange-haired teenager named Ichigo, who becomes a Shinigami, which roughly translates as a “death god”-- like the Grim Reaper in western tradition-- which sends departed souls to the afterlife in “Soul Society”. Some of these lost souls turn into “Hollow”, evil spirits which accumulate power by consuming other lost souls and occasionally will turn to attack humans. This serves as a never ending source of conflict for the wide cast of Shinigami to fight off evil in extravagant action sequences. Each of the colorful characters is complemented with a unique weapon called a Zanpakutou which would is considered to be a manifestation of the wielder's soul in a sword.

This relationship between the Shinigami and the Zanpakutou has several qualities about it that remind me of Julian Jaynes's Bicameral Mind. The Shinigami are portrayed as conscious actors, in a Jaynesian sense, while the Zanpakutou represent their unconscious instincts to fight and kill. A recurring theme in the series is that Ichigo's instincts tend to take over in times of severe distress, but he gradually improves at harnessing the Zanpakutou consciously to control the amount of devastation unleashed. The universe of Bleach is one of fiction, but much like Jaynes considers language of the Iliad as a metaphor for the mind of the ancient Greeks, might modern fiction also serve as a metaphor for modern social perceptions of consciousness? I'm going to focus primarily on the bicameral nature of the Shinigami-Zanpakutou relationship, but I'd note that Ichigo represents a slightly more complex model that still has the potential to revert to this bicameral state.

The first thing to note is that Jaynes' model of consciousness is not the same as awareness, as it is commonly used in language but rather refers to something a bit more technical. There are four key features of Jaynes Consciousness (J-Con): (1) an analog “I”, (2) a metaphor “me”, (3) inner narrative, and (4) introspective mind-space. These four features enable an individual to “test” potential behaviors in the mind-space before trying them out in the real world. In contrast, an “unconscious” being acts instinctively and is immediately focused on the “here and now”. The reason I think Bleach is a great example of J-Con is because Ichigo's Hollow form personifies the “unconscious” mind and poses a stark contrast to the behavior of Ichigo while he is “conscious”.

Ichigo's consciousness normally resides in his human body, but when he becomes a Shinigami, his consciousness separates from his physical body. His analog “I” and metaphor “me” are manifested in his Shinigami form. Shinigami can influence their environment, including damage and destruction, and can be also be influenced by their environment, including injury and death. Ichigo is often portrayed narrating fights, consciously breaking apart his opponents fighting style. When Ichigo's Hollow takes over, he doesn't bother so much with reading his opponent. He just attacks relentlessly with no concern for how much damage is caused. Ichigo's conscious mind strives to suppress and control this instinct, so that he may uses its power to protect his friends. Ichigo's internal mind-space is depicted visually at various points in the series. Ichigo's world resembles a sideways metropolis. In one of my favorite episodes, Ichigo literally fights against his Hollow self within this inner world.

Now that I've established what J-Con is, the next thing I need to define is the bicameral mind. Jaynes argues that prior to the development of J-Con, human beings behaved according to auditory hallucinations originating from the right hemisphere of the brain which commanded them to act. These hallucinations were often perceived to be the voices of “gods” or “ancestors”, and commanded the individual to act. This mode of thinking is very similar to the behaviors of schizophrenics in modern times. In hypnosis, the analog “I” gives up its power to an outside authority and the body follows this sources command. In the schizophrenia and bicameral mind, this authority is a hallucination.

In Bleach, the Zanpaktou often calls out to its Shinigami master through dreams. In the case of Captain Hitsugaya, he had a recurring dream of an icy dragon calling out to him, but he could not hear its name. When he finally heard its name, that's when he became a Shinigami. The Zanpaktou is often portrayed as its own person, but resides within the soul of its Shinigami. Shinigami become more powerful by communicating with the Zanpaktou. When Shinigami and Zanpaktou fight as one, they come closest to meeting their full potential.

While not part of the manga, episode 255 of the anime involves a fight between Ichigo and Muramasa, a Zanpaktou with powers of hypnosis. Zangetsu, Ichigo's Zanpaktou, speaks to him:

“Ichigo Feel him” “Zangetsu?” “His hypnosis no longer works on me. I shall be your eyes. But for this to work, we must truly communicate with one another as master and Zanpakutou.” “I understand, old man” (Bleach ep255)

The fight with Muramasa starts to turn around. When Ichigo gains the upper hand, he confesses the change to Muramasa:

“I finally understand what he's been trying to tell me.” “What?” “We have to acknowledge each other's existence and accept one another. That's how Zanpakutou and Shinigami are supposed to interact.” (Bleach ep255)

I feel that this communication between Shinigami and Zanpaktou is much like the bicameral state of mind described by Jaynes. When communicating with Zangetsu, Ichigo does not descend entirely into instinctive behavior, as he does in Hollow form, but rather becomes aware of these instincts and uses them to obtain his goals. Much like bicameral humans followed the commands of auditory hallucinations, Ichigo enters a state of mind where Zangetsu dictates his actions. The wall separating Zangetsu from Ichigo's analog “I” dissolves to a point where the two parts of his mind act as one. In fights such as the one with Muramasa, the part that is Zangetsu dictates the behavior while the part that is Ichigo listens and obeys. This bicameral state is where Ichigo's power is greatest.

In the Origin of Consciousness, Jaynes finds support for this theory in the language of the Illiad. In the Illiad, the gods dictated the behavior of the actors. In contrast, the Odyssey presents actors which behave on their own accord. Jaynes argues that this change reflects the development of J-Con taking place in that period. If anything is to be learned from Bleach, it's that modern culture acknowledges both modes of thinking. While humans generally exhibit behavior consistent with J-Con, the bicameral state is still partially accessible to the mind. As human beings, we need to accept that we have certain instincts. Consciousness provides us with the power to observe these instincts, and choose when and how they manifest themselves.

Ichigo's story suggests that although humans are still capable of this bicameral state, there are risks associated with entering it. Ichigo's Hollow self and Zanpaktou are closely related. In relying on his Zanpaktou's powers, Ichigo runs the risk of his instincts taking over. While Ichigo obtains power by descending into a bicameral-like state, he needs to make sure that he doesn't completely relinquish conscious control over his actions. Hollow Ichigo says that he is the “horse” and Ichigo is the “king”, but if Ichigo were to let his guard down he will be quick to “take the crown” (Bleach manga 221). In essence, the Hollow Ichigo represents what would happen if Ichigo descended completely into bicameralism. In bicameral individuals, the hallucination is the “king” and the self is the “horse”.

I picked up Mark Bauerlein's The Dumbest Generation: How the Digital Age Stupefies Young Americans and Jeopardizes Our Future * or Don't Trust Anyone Under 30 (DG) yesterday and have been up all night reading it. Not because I enjoyed it, but because it made me angry. I should have anticipated this, considering how I'm 27 and the sub-title of the book is “Don't Trust Anyone Under 30”. I'm a part of the generation Bauerlein is talking about, and I consider this book a biased pseudo-scientific misrepresentation of myself and my peers.

It's important to note that I probably represent a fringe case within the generation. I read regularly and tend towards non-fiction literature. The fact that I bought this book in the first place is evidence that I'm an outlier. I play several musical instruments, saxophone and guitar being my favorites. I taught myself how to program in high school and designed websites for local businesses. I started out as a Math Major in college, but eventually double majored in Mathematics and Psychology because I was fascinated with learning how the human mind works. After graduating, I pursued another love of mine, video games, and landed a job as a programmer at a game studio. After a few years, I decided that I wanted to make video games that fostered the development of critical thinking skills. I enrolled myself in graduate school and started teaching remedial math. I'm also a complete technophile, love the latest gadgets and gizmos, and can't stand more than a day without being connected to the Net.

Bauerlein talks quite negatively of video games, and I don't think this criticism is well founded. There's a substantial amount of mathematics that can be found in video games. Gamer communities like the Elitist Jerks (http://elitistjerks.com) use spread sheets and simulation programs to mathematically optimize stats and equipment in World of Warcraft. These massively multiplayer online games are complex mathematical systems, complete with virtual economies and social interaction. “Casual” players might not experience the same depth of content, but the “hardcore” players participate in a substantial amount of meta-gaming and often reflexively analyze their performance to foster continued improvement. I think its unfair to devalue competitive video gaming as simply a leisure activity; I consider such play to be equally as intellectual as playing Chess or Go. I would also note the considerable amount of mathematics, science, and art involved in making the video game itself. From my personal experience, learning to play and create video games directly contributed to my interest in math, science and engineering. There are a myriad of video games that are trivial and superficial, but there are also games I would call “higher art” that challenged my perceptions about storytelling in an interactive medium. Bauerlein doesn't even address the topic of video games as “higher art”. He treats the entire medium as if it were completely devoid of any social value altogether.

What kinds of media does Bauerlein suggest in video games' place? A variety of gems including Harry Potter, Dante, Milton, A Christmas Carol, Rush Limbaugh, Fox News, and the Bible. Bauerlein tries to portray the problem as a cultural war, but these repeated references to religiously themed works also reveal an ideological difference. These were probably intended as generic books and news sources, but the choices used show a pattern of right-wing religious bias. The whole argument is framed like a dichotomy between the conservative-religious-elders and the liberal-secular-youth, as personified by technology. It appears like Bauerlein is more upset about students not reading his culturally biased list of literature than he is about the real faults of our nation's education system.

These are bold claims, but there are good reasons to be skeptical of DG. The information is all second-hand, and no new research is presented. The data that is presented is not even organized into a coherent framework. It reads like series of disconnected statistics are piled on, one after the other, with no consistency in procedure. In themselves, they each sound like reasonable results. However, the data is mostly tangent to the central thesis about the role technology in producing these trends. It gradually turns into “proof by verbosity”, focusing largely on differences in cultural and ideological values which are not scientifically falsifiable hypotheses to begin with. The book repeatedly references “tradition” as an authority, as if the previous generation has some mysterious source of ancient wisdom. Science is conducted in the open. Clinging onto ideas out of tradition alone is not the way to foster progress.

There are a couple of points in particular that seem suspect. First, the inconsistency between falling rates of factual recall and increasing averages on IQ tests. Memorization skill and Intelligence are two entirely separate constructs. The obvious explanation for this phenomena is that the collection of information worth memorizing has changed but general problem solving ability hasn't. The largest drop in the included performance statistics seemed to take place after the turn of the millennium, which is also a bit suspicious given 2001 passage of the No Child Left Behind Act of 2001. It's difficult to compare data from before and after a major legislative change which mandates changes in how student performance is assessed and how teachers teach. There is not enough data here to rule out the interaction of other changes in the educational process as an alternative explanation. In a scientific study, the data should speak for itself. The data presented in DG shows that there is significant need for improvement in education, but it's not enough to indict technology as the singular cause of the problem.

Another point worth making is that DG suffers from a combination of selection and actor-observer biases. In defending Generation M, I'm partially guilty of this myself. I'm an intellectual person and tend to associate with like-minded people. Thus, I have a tendency to generalize the behaviors my peer group appears to the generation as a whole. I think Brauerlein is guilty of this also. He probably tends to associate with the intellectual types and may therefore incorrectly generalizes this intellectualism to his generation as a whole. The second fallacy here, is that there is also a tendency to attribute observed behaviors to personality traits instead of the situation. As Brauerlein acknowledges, it's not unusual for teens to go through a rebellious phase, and the technology usage might just be an expression of this. Consider another option: What if Gen M-ers are being honest when they say the information they're being taught isn't relevant to their lives? Certainly these questions merit additional consideration.

This is a commercial product, which is intended to sell copies, rather than a peer-reviewed study in a scientific journal. The reviews on book cover are all from popular media sources rather than the scientific community. Some of Bauerlein's statistics are certainly interesting, but I don't think they demonstrate anything close to a causal relationship between technology usage and intelligence. He doesn't bother to define “intelligence” and tends to use it interchangeably with “knowledge”. I would have also liked to see an effort to normalize the data and plot it over time in comparison to technology usage rates. He cites plenty of sources showing a deficiency in these skills, but there are still too many external factors to point to technology as the source of the problem. The fact that learners process web information differently than print materials just shows that the two mediums need different approaches.

The language of the book is highly emotionally charged and features numerous stereotypical persuasive devices. It identifies a common enemy for the readers to rally against, uses cultural references to which older readers would relate closely, and tries to make the readers feel like a part of something larger than themselves. Even the choice of title and cover art seems like it was designed to trigger an emotional response rather than promote rational intelligent discourse. I found it particularly interesting how Bauerlein tries to present jazz as a higher art form in opposition to modern rap and rock. The irony is that jazz was all about “breaking the rules”, reversing the established chord progression, and eventually laid the foundation for the modern music which Bauerlein seems to despise so thoroughly.

During my undergraduate study, there were times where I found myself relearning subjects from new perspectives. Gödel's Incompleteness Theorem completely changed how I thought about mathematics and computing. The theorem states that any fixed formal axiomatic system will have statements that are neither provable or disprovable in that system. Math ceased being about prescribed procedures and memorization and turned into an exploration of how different sets of hypothetical rules might behave. It stopped being about blindly following the rules and instead tolerated the bending or even breaking of them. Part of me wished math could had been that way from the beginning. I wanted to provide the “past me” with a variety of different sets of rules and allow me to explore how they work in a controlled environment. That's precisely why I think Games have such potential as a educational medium. They don't need to be Video Games. Board, Card, Dice and Pen & Paper Games have very beautiful and complex mathematical structures lurking just below the surface of the rules.

My active rejection of the traditional values is different from a passive indifference as implied by DG. I might be a statistical anomaly in this cohort, but I don't think I'm alone. Brauerlein might reject the notion that the problem is in the situation and not the students, but my experiences showed me that many things presented as “facts” in middle/high school were quickly replaced by better models in college. Newtonian Physics became M-theory, Math became Meta-Math, and Technology Use evolved into Software Engineering. DG suggests that the curriculum is not “hard” enough, so maybe we just need to stop diluting the truth? I wish I had Logic and Set Theory as topics in grade school. I want “past me” to be allowed the opportunity to build a solid foundation for the “real” math I'll encounter in the “real” world. I don't want to “learn the wrong way now, learn the right way in college”. Why should I trust an authority figure that routinely hides the truth from me because “its too hard”?

I'm Ryan and this is my blog. This is the place where I can speak my mind about anything and everything without having to worry about that pesky 140 character limit on Twitter. Here you can find my unadulterated opinions of life, math, religion, politics, education, video games, books, movies or whatever else I happen to find interesting at the moment. These opinions are my own, and do not necessarily represent the opinion of my employer, my political party, or anyone else for that matter.

Why "Suburban Lion"?

Party because of a childhood nickname, "Ryan the Lion", and partly because of a line from an Oingo Boingo song called "Pedestrian Wolves".